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Transformation of Functions
231–235 Describe the transformations from the f function to the g function.
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Transforming Selected Points Using Functions
236–240 Transform the points (3, 4), (–2, 6), and (5, –1) using the function description of the transformations.
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Sketching Graphs Using Basic Functions and Transformations
241–245 Find the vertex of the given function, which is a transformation of
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Sketching More Graphs Using Basic Functions and Transformations
246–250 Find the vertical asymptote of the given function, which is a transformation of
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Chapter 5
Polynomials
Polynomial functions have graphs that are smooth curves. They go from negative infinity to positive infinity in a nice, flowing fashion with no abrupt changes of direction. Pieces of polynomial functions are helpful when modeling physical situations, such as the height of a rocket shot in the air or the time a person takes to swim a lap depending on their age.
Most of the focus on polynomial functions is in determining when the function changes from negative values to positive values or vice versa. Also of interest is when the curve hits a relatively high point or relatively low point. Some good algebra techniques go a long way toward studying these characteristics of polynomial functions.
The Problems You’ll Work On
In this chapter, you’ll work with polynomial functions in the following ways:
Solving quadratic equations by factoring or using the quadratic formula
Rewriting quadratic equations by completing the square
Factoring polynomials by using grouping
Looking for rational roots of polynomials by using the rational root theorem
Counting real roots with Descartes’s rule of signs
Using synthetic division to quickly compute factors
Writing equations of polynomials given roots and other information
Graphing polynomials by using end-behavior and the factored form
What to Watch Out For
Don’t
